Question: Find the value of the following expression:

$$\left| \, |{ -|{-1 + 1}| - 1 }| + 1\right|.$$
Solution: We calculate as follows: $$|\,|{-|{-1+1}|-1}|+1| = \left|\, |0-1|+1\right| = |1+1| = \boxed{2}$$